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Thursday, December 8, 2011

Confirmation that Mandelbrot Beats Standard Economic Theories

Nassim Taleb gets much credit for popularizing the idea that big economic events, so-called “black swans,” occur more frequently than standard economic theory predicts. The initial work was actually done by the “father of fractals,” Benoit Mandelbrot.
Physicists have studied detailed market data and have now concluded that Mandelbrot was right. (Hat tip to the Stingy Investor for pointing me to this article.)

The bigger the market move we contemplate, the lower the chances that it will happen. However, these probabilities shrink much more slowly than standard economic theory predicts. In standard economic theory based on the normal distribution, if a move has a 1 in 1000 chance of happening, a move twice as large has less than a 1 in a billion chance of happening. In Mandelbrot’s model as confirmed by the physicists, the bigger move has about a 1 in 8000 chance; each doubling in move size reduces the odds by 8 times.

For conditions of low market volatility, standard theory and Mandelbrot’s model agree fairly well, but when it comes to the possibility of big upheavals, standard theory is just plain wrong.

@Mark: For investors who are likely to panic and sell at a bad time, this research suggests that they should be a little more conservative with their portfolios than standard theory would suggest. One way to do this is with asset allocation. Another is with options. However, I've never been able to make the numbers work using options to reduce downside risk. Every time I try to build a real portfolio incorporating options the cost of the downside protection seems far too high.